Calculation of Shocks with Skew Symmetric Schemes

We present a fully conservative finite difference scheme for the compressible Navier—Stokes equations with shocks. Building on a skew symmetric form of the transport term in the momentum equations the kinetic energy is perfectly conserved by this transport term, as in the analytic theory; the kinetic energy is only changed by pressure or explicit added friction. Due to this stable simulations are possible without physical or artificial damping away from shocks; at shocks adaptive damping is introduced. The scheme is especially suited for the simulation of configurations where perfect conservation is needed along with low damping, e.g. shock—acoustic interactions. The full conservation along with the perfect skew symmetry is also preserved for arbitrarily transformed grids. We focus on technical aspects of shock calculations and the theoretical justification.